Expansion joints may be used in a number of different types of assemblies, based upon the application. Various assemblies are described and sample models thereof are shown. (Note that CAESAR II provides an expansion joint modeling feature which can automatically build many of the expansion joint assemblies shown here. It is accessed by pressing J at the piping input spread sheet.)
Hinge expansion joints are shown in Figure 3-46.
The hinges restrict angular rotation of the bellows to a single plane, and may be used in a single- or double-hinged configuration, the latter of which comes as a single unit. When using a pair of single hinged joints, the joints should be placed as far apart as possible to reduce angular rotations as well as forces and moments. In most cases, the hinges are designed to pass through the full pressure thrust load, so there is no need for tie rods. In some cases, the hinge connections may be slotted to permit axial displacement of the bellows, however, then the pressure thrust must be absorbed by adjacent anchors. A typical hinge application is shown in Figure 3-47. Note that the piping system requires bending in one plane only.
A computer model for a single hinge expansion joint is shown in Figure 3-48.
Gimbal expansion joints are shown in Figure 3-49.
Gimbals are designed to permit angular rotation in any plane. The hinges and gimbal ring are capable of absorbing axial pressure or vacuum loads, dead weight of adjacent piping, and torsional moments. Like hinges, if gimbals are used in pairs, they should be located as far apart as possible to maximize absorbed displacement, and reduce rotation and forces and moments. A typical gimbal joint application is shown in Figure 3-50. Note that the piping system requires bending in two planes.
A computer model for a gimbal joint, such as the first one shown in Figure 3-49 is very simple to build — one simply defines an expansion joint with rigid axial, lateral, and torsional stiffnesses, and a bending stiffness equal to that of the actual expansion joint used, since the gimbal is free to bend in all directions. (Rigid elements with weights equal to the weight of the gimbal assembly may be included as well.) Sometimes, however, a gimbal may be used in conjunction with hinges, as shown in the diagram of the angular/transverse joint in Figure 3-49. A computer model for something like this is more complex to build — one solution is shown in Figure 3-51.
The hinges/gimbal are modeled as the rigid series of elements running from 10 to 45 along the top of the figure, while the bellows and spool piece are modeled as the elements running along the bottom of the figure. Element 10 to 15 is a rigid element, having a length equal to the distance from the face of the inlet flange to the axis of the first hinge, with a weight equal to approximately one-quarterof the total weight of the hinge/gimbal hardware (note that fluid and insulation weight is automatically added to non-weightless rigid elements, so that should be considered when assigning a weight to these elements). The hinge (element 15 to 20) is modeled as a zero-length expansion joint with rigid (IE 12) axial, lateral, and torsional stiffnesses, and a bending stiffness of 1 (which is effectively zero). The hinge is restricted to one-directional rotation by restraining node point 15 rotationally about the X-axis, with a CNODE of 20. Element 20 to 25 is another rigid element, having a length equal to the distance from the axis of the first hinge to the mid-point of the gimbal, and again a weight equal to one-quarter of the total hardware weight. The gimbal (element 25 to 30) is a zero-length expansion joint with rigid axial, lateral, and torsional stiffnesses, and a bending stiffness of 1 (unrestricted by any restraints). Element 30 to 35 is a third rigid element, having a length equal to the distance from the mid-point of the gimbal to the axis of the second hinge (again with one-quarterof the total hardware weight). The second hinge (element 35 to 40) is modeled in the same way as the first, except that the rotational restraint applied at node point 35 is about the Y-axis, with a CNODE of 40. The final rigid element, from node point 40 to 45, has a length equal to the distance from the axis of the second hinge to the face of the outlet flange, and provides the final quarter of the hardware weight. Since neither the hinges nor gimbals are internally pressurized, the expansion joints which are used to model them should be given effective diameters of zero as well.
The expansion joints and spool piece will be modeled from node point 10 to 45 as well, indicating that the centerlines of the two assemblies are coincident, but connections are present only at the end points. Elements 10 to 1015 and 1040 to 45 are rigid elements with the length and weight of the two end flanges. Elements 1015 to 1020 and 1035 to 1040 are finite length expansion joints modeled with the exact properties of the actual bellows used (including effective diameter). Element 1020 to 1035 is modeled as a normal pipe element, representing the spool piece between the two expansion joints.
A universal expansion joint is shown in Figure 3-52.
Universal joints consist of two unrestricted expansion joints flanking a spool piece. They are usually used to absorb large lateral movements in any direction. By increasing the length of the center pipe the amount of lateral displacement absorbed can be increased, with a corresponding reduction in the lateral forces and bending moments. In most cases universal joints are tied to prevent the pressure from blowing apart the assembly. (When a universal expansion joint must absorb axial movement other than its own axial growth, an untied universal should be used—in that case, adjacent restraints must be designed to handle the pressure thrust.) A center support may be provided on the tie rods to help support the weight of the center piece, to provide limit stops for the displacement, and/or to reduce the length of compressive rods (and the corresponding tendency of the rods to buckle).
A simple model of a universal expansion joint is shown in Figure 3-53.
Since the tie rods isolate the pressure loads and thermal axial growth of the joint from the remainder of the system, the assembly can be simply modeled by calling the effective diameter of the bellows zero, the axial stiffness of the bellows rigid, and the temperature of the assembly ambient. Elements 4 to 5 and 1006 to 7 are rigid elements (with the weight of the tie rods, etc.), elements 5 to 1005 and 6 to 1006 are expansion joints with effective diameters of zero, axial stiffness of rigid, and bending and lateral stiffnesses as determined from the manufacturer. Element 1005 to 1006 is simply a pipe element representing the spool piece. The total length of the elements from node point 4 to node point 7 should be the same as the length of the tie rods, and, as noted above, the assembly should all be set to ambient temperature.
More complex models involve entering as accurately as possible the bellows, tie rods, and all supporting mechanisms. These models are very cumbersome to build but will give the most accurate representation of the loads, movements, and other conditions in and around the joint. More complex universal joint models are shown in Figure 3-54.
Other expansion joint configurations may be modeled by modeling various combinations of bellows, hinges, gimbals, tie rods, limit stops, and other hardware as shown in these figures. A more accurate (and more likely correct) representation of the real configuration can usually be achieved with a more complex model. When modeling the assembly, total hardware weight must be considered, including internal or external sleeves and bellows end connection details, in addition to the items noted above.
Modeling And Analysis Of The Piping System
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